Question: Solve for $x$ : $4\sqrt{x} - 9 = 7\sqrt{x} + 9$
Solution: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} - 9) - 4\sqrt{x} = (7\sqrt{x} + 9) - 4\sqrt{x}$ $-9 = 3\sqrt{x} + 9$ Subtract $9$ from both sides: $-9 - 9 = (3\sqrt{x} + 9) - 9$ $-18 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-18}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-6 = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.